 |
Bert Gerards Centrum Wiskunde & Informatica |
bert.gerards@cwi.nl
phone +31644207040 |
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| publications | some talks | ||
| third workshop on graphs and matroids, maastricht, 29 july - 3 august 2012 | |||
| I work in combinatorial optimization, an area on the interface of mathematics and computer science that seeks to find efficient algorithms for discrete computational problems. |
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My main research interest is Matroid Theory.
Jim Geelen,
Geoff Whittle and I
work on generalizing Robertson and Seymour's Graph Minor Theory to
matroids representable over finite fields.
Two of the three main targets of this project are the following
conjectures by Robertson and Seymour:
• Matroids representable over a fixed finite field are well-quasi-ordered by minors. • Any minor-closed property can be tested in polynomial time for matroids representable over a fixed finite field. Our main result so far is that these are true for binary matroids. Scientific challenge and bulk of the work here is to understand the structure of minor-closed classes of matroids over the field at hand. In general this is still not fully done, but recently we bridged the conceptually major remaining gap between prime fields and the general non-prime case by giving the structure around large projective geometries. Understanding structure may also yield our third goal: Rota's conjecture. |
| I am also part-time professor at the Department of Quantitative Economics of Maastricht University School of Business and Economics and adjunct professor in the Department of Combinatorics & Optimization of the University of Waterloo. |
| Recent postdocs of mine are: Tony Huynh and Stefan van Zwam. |